sqrt2norm.m

function pts = sqrt2norm(pts,type,nv)
arguments
    pts double {mustBeNumeric,mustBeFinite}
    type char {mustBeMember(type,{'oct','quat'})} = 'oct'
    nv.warnQ(1,1) logical = true
end
% sqrt2norm  take a set of octonions and give each row norm == sqrt(2) if (norm == 1) || (norm == sqrt(2))
%--------------------------------------------------------------------------
% Author: Sterling Baird
%
% Date: 2020-07-27
%
% Description: a
%
% Inputs:
%		a -	a
%
% Outputs:
%		b -	b
%
% Usage:
%		a = b(a);
%
% Dependencies:
%		*
%
% Notes:
%		*
%--------------------------------------------------------------------------
tol = 1e-2;
warnQ = nv.warnQ;
switch type
    case 'quat'
        % if norm(o) == 1 within tolerance, multiply by sqrt(2)
        if all(abs(vecnorm(pts(:,1:4),2,2)-1/sqrt(2)) < tol) ...
                && ...
                all(abs(vecnorm(pts(:,5:8),2,2)-1/sqrt(2)) < tol)
            
            %fine, no warning
            
        elseif all(abs(vecnorm(pts(:,1:4),2,2)-1) >= tol) ...
                || ...
                all(abs(vecnorm(pts(:,5:8),2,2)-1) >= tol)
            
            if warnQ
                warning(['norm(qA) == ' num2str(norm(pts(1,1:4))) ', ' ...
                    'norm(qB) == ' num2str(norm(pts(1,5:8))) ...
                    '. norm of 1+ quaternions ~= 0.7071 || 1'])
            end
        end
        pts(:,1:4) = normr(pts(:,1:4));
        pts(:,5:8) = normr(pts(:,5:8));
        
    case 'oct'
        ptnm = vecnorm(pts,2,2);
        if ~isempty(find(ptnm == 0, 1))
            %            warning('identity octonion(s) present')
            ptnm(ptnm == 0) = [];
        end
        if all(abs(ptnm - 1) < tol)
            %fine, no warning
        elseif any(abs(ptnm - sqrt(2)) >= tol)
            if warnQ
                warning('norm of octonions ~= 1 || sqrt(2)')
            end
        end
        pts = normr(pts)*sqrt(2);
end

end